Comparing TODIM and CPT-TODIM for Social Sustainability Assessment in G7 Countries

Vaishnudebi DuttaSubhomoy Haldar
ByVaishnudebi Dutta and Subhomoy Haldar•
research publications academic mcdm decision-making sustainability prospect-theory

Background

This paper came from a question we asked: if you want to rank countries on how “socially sustainable” they are, which algorithm should you use? Many multi-criteria decision-making (MCDM) algorithms exist, yet most research focuses on a single one. We wanted to dig deeper.

We focused on TODIM and its enhanced variant CPT-TODIM because they’re based on prospect theory. People are more affected by losses than by gains, as the Nobel Prize-winning idea suggests. This makes them well-suited for decisions where subjective judgement matters.

The Problem in Plain English

Suppose you want to rank the G7 countries (Canada, France, Germany, Italy, Japan, UK, USA) on social sustainability. You have 14 criteria: average wage, employment rate, income inequality, women in politics, education levels, and so on. How do you combine all these numbers into a single ranking?

Most algorithms work by computing a “distance” to some ideal solution. The country closest to the ideal wins. The problem is that by compressing all that multi-dimensional data into a single distance score, you lose nuance. Two very different countries might end up with similar distances, making the ranking unstable.

TODIM takes a different approach. Instead of evaluating countries based on their distance from a theoretical ideal, this method involves a criterion-by-criterion comparison of every country. For each pair, it asks: “Is Country A better or worse than Country B on this criterion? By how much?” Then it weighs losses more heavily than gains (because that’s how humans think). The result is a more stable ranking that doesn’t flip the alternatives around when you add or remove options.

CPT-TODIM extends this by adding parameters that model risk attitudes more precisely. It transforms the criterion weights using cumulative prospect theory, giving decision-makers finer control over how gains and losses are perceived.

Measuring Rank Reversals

We assessed algorithm stability through rank reversal analysis. Rank reversal occurs when removing one option changes the ordering of the remaining choices. We tested each algorithm by removing one G7 country at a time and checking if the remaining rankings shifted:

AlgorithmRank Reversals (out of 7 removals)
CoCoSo4 (FR, IT, JP, USA removals)
TODIM2 (CA, DE removals)
CPT-TODIM1 (DE removal only)

CoCoSo proved unreliable, with more than half of removals causing rank reversals. Both TODIM variants displayed minimal reversals, with CPT-TODIM being the most stable.

Abstract

Social sustainability objectives within the framework of sustainable development goals (SDGs) are critical aspects of balanced societies. Governments must constantly assess their performance to accomplish social sustainability goals. This paper evaluates the performance of seven industrialised nations: members of the Group of Seven (G7), in a streamlined manner. The rank sum weighting approach was used to quantify the subjectivity of experts’ judgements. In order to assess social sustainability performance for G7 countries, TODIM (TOmada de Decisão Interativa e Multicritério) and Cumulative Prospect Theory TODIM (CPT-TODIM) are implemented to compare the social sustainability performance of the G7 nations. Furthermore, sensitivity analysis is performed over 1000 different weight permutations of the criteria and alternatives from the original roster are removed to evaluate and contrast the two Multi-Criteria Decision-Making (MCDM) algorithms used to gain a deeper understanding of the strengths and limitations of each approach such as rank reversal problem. This analysis has also led to the conclusion of CPT-TODIM outranking both TODIM and CoCoSo algorithms. Analysis of 2020 OECD iLibrary data using both algorithms revealed that France emerged as the most socially sustainable country among the G7 nations.

Publication Details

Authors

Keywords

Social sustainability, multi-criteria decision-making, prospect theory, TODIM, CPT-TODIM, sensitivity analysis

Code and Data

The Python code for running the comparative and sensitivity analysis is available on GitHub: Coders-Compass/social-sustainability

The study uses 2020 data from the OECD iLibrary.

Access the Publication

The full paper is available through the DOI link above. It contains the complete mathematical derivations, sensitivity analysis heat maps, and policy implications for each G7 country.

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